Incidence structures and Stone---Priestley duality

Authors:
Mohamed Bekkali;Maurice Pouzet;Driss Zhani
Affiliations:
Département de Mathématiques, Faculté des Sciences et Techniques, Université Sidi Mohamed Ben Abdellah, Saïss-Fè, Morocco;PCS, Université Claude-Bernard Lyon1, Lyon cedex 07, France 69365;Département de Mathématiques, Faculté des Sciences et Techniques, Université Sidi Mohamed Ben Abdellah, Saïss-Fè, Morocco
Venue:
Annals of Mathematics and Artificial Intelligence
Year:
2007

Citing 1
Cited 3

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Abstract

We observe that if R:驴=驴(I,驴, J) is an incidence structure, viewed as a matrix, then the topological closure of the set of columns is the Stone space of the Boolean algebra generated by the rows. As a consequence, we obtain that the topological closure of the collection of principal initial segments of a poset P is the Stone space of the Boolean algebra Tailalg (P) generated by the collection of principal final segments of P, the so-called tail-algebra of P. Similar results concerning Priestley spaces and distributive lattices are given. A generalization to incidence structures valued by abstract algebras is considered.